Question

If a right triangle has sides 5, 12, and 13 units, then a triangle with sides 10, 24, and 26 is also a right triangle. (1 point)

True, because multiples of a right triangle triple produces a similar right triangle with congruent angles.

False, because doubling the sides of the triangle does not keep the angles congruent.

Answer 1

Are you sure explain

Answer 2

Okay thanks

Answer 3

True, because the sides of the second triangle are all double the sides of the first triangle, so their proportions remain the same.

Answer 4

I apologize for the mistake in my previous response. Let's consider the given right triangle with sides 5, 12, and 13 units.

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, it would be

5^2 + 12^2 = 13^2

25 + 144 = 169

169 = 169

Since the Pythagorean theorem holds true for this triangle, it is a right triangle.

Now, for the triangle with sides 10, 24, and 26 units, let's apply the same logic:

10^2 + 24^2 = 26^2

100 + 576 = 676

676 = 676

Since the Pythagorean theorem also holds true for this triangle, it is also a right triangle.

Therefore, the statement "If a right triangle has sides 5, 12, and 13 units, then a triangle with sides 10, 24, and 26 is also a right triangle" is true.

Answer 5

You're welcome! If you have any more questions or need further clarification, feel free to ask. I'm here to help!